Well, at first Harry might be very suspicious. But as Snape shows consistent care, Harry could start to see him in a new light. Maybe he realizes that Snape has more layers than he thought. He might begin to understand that Snape's past actions were more complex than just being mean to him.
Well, it could be about Snape feeling a sense of duty. Maybe after Harry loses his sight in a battle against the Dark Arts, Snape, despite their past differences, steps in. He might start by teaching Harry new ways to navigate Hogwarts using magic that doesn't rely on sight, like advanced sonar - like spells.
One common scenario is Snape protecting Harry from the Dark Arts attacks within Hogwarts. Another could be Snape helping Harry with his studies privately, especially in potions where Snape is an expert.
Another option is to join Harry Potter fan groups on social media platforms like Facebook or Reddit. Ask the members if they know of any fanfics with this plot. They might be able to point you in the right direction. Sometimes, fans share their favorite or newly discovered fanfics in these groups.
There might be a fanfiction where Harry takes care of Snape after a battle. He could be the one to tend to Snape's wounds, both physical and emotional. Since Snape has always been a rather closed - off character, Harry's attempts to get through to him and provide care could be a great source of character development for both of them. Harry might use his Gryffindor courage to break down Snape's walls.
You can try looking on Archive of Our Own (AO3). It has a vast collection of Harry Potter fanfictions, and it's likely that you'll find several stories about Harry taking care of Snape there. Just use the search function and type in relevant keywords like 'Harry takes care of Snape' and you should get a list of relevant fics.
It's popular because it creates an interesting dynamic. Snape has always had a complex relationship with Harry in the original series. When Harry is deaged, it gives Snape a chance to start anew and perhaps be a different kind of influence. It also allows for exploring Snape's more nurturing side which is a contrast to his usual cold persona.
There's 'Snape and the Deaged Savior'. In this fanfiction, Snape discovers deaged Harry in an unexpected place. He takes on the role of caretaker with his usual grumpy exterior but deep down shows a lot of care. He teaches Harry magic in a different way than the normal Hogwarts curriculum, which makes for an interesting read.
One possible plot could be that Harry discovers a time - traveling accident has brought baby Snape to his present. Harry, being the kind - hearted person he is, takes it upon himself to care for the baby. He has to figure out how to feed the baby, keep him clean and comfortable. Maybe he also has to protect baby Snape from any threats in the wizarding world that might target Snape even as a baby.
One common theme is redemption. Snape is often seen as a character in need of redemption in the original series, and taking care of Harry can be a way for him to achieve that. Another theme is the exploration of family. It shows a different kind of family dynamic than the traditional ones in the Harry Potter world. And there's also the theme of sacrifice. Snape might have to sacrifice his own interests or safety to protect Harry.